Question

The denominator of a rational number is greater from its numerators by 10. If the numerators is increased by 19 & the denominator is decreased by 1. The number obtained is $\frac{3}{2}$. Find the rational number.

• A. $\frac{1}{11}$
• B. $\frac{7}{17}$
• C. $\frac{11}{21}$
• D. None of these

Answer 1

The correct option is C $\frac{11}{21}$

Let the numerator be $x$.

$\Rightarrow$ Then, denominator will be $=x+10$

According to the question,

$\Rightarrow$ $\frac{x+19}{x+10-1}=\frac{3}{2}$

$\Rightarrow$ $\frac{x+19}{x+9}=\frac{3}{2}$

$\Rightarrow$ $2(x+19)=3(x+9)$

$\Rightarrow$ $2x+38=3x+27$

$\Rightarrow$ $x=38-27$

$\Rightarrow$ $x=11$

$\Rightarrow$ The required rational number $=\frac{x}{x+10}=\frac{11}{11+10}=\frac{11}{21}$